1. Technical Field
Generally, the present disclosure relates to the field of fabrication and usage of logic gates, for instance for computing and controlling purposes, wherein alternative methods for generating and propagating binary signals in the form of quantum cellular automata (QCA) are employed.
2. Discussion of the Related Art
Immense progress has been made in the field of semiconductor production techniques by steadily reducing the critical dimensions of circuit elements, such as transistors, in integrated circuits. For example, critical dimensions of 30 nm and less have been implemented in highly complex logic circuitry and memory devices, thereby achieving high packing density. Consequently, more and more functions may be integrated into a single semiconductor chip, thereby providing the possibility of forming entire systems on chip so that highly complex electronic circuits may be formed on the basis of a common manufacturing process. Complex integrated circuits that are produced on the basis of volume production techniques are mainly based on CMOS technology using silicon as semiconductor base material due to the many advantages of silicon in terms of availability, costs, and the like. On the other hand, intrinsic characteristics of a silicon-based semiconductor material, such as reduced charge carrier mobility, and the like, impose an ever increasing burden on well-established CMOS technology, since any advances in performance of silicon-based devices are typically dependent on a significant reduction of the critical dimensions of the basic transistor devices used. Therefore, there is an ongoing search for new materials that may efficiently replace the silicon base material for the fabrication of powerful yet cost efficient complex integrated circuits.
On the other hand, alternative approaches have been discussed for a long time, for instance with respect to increasing the overall computational power of computer devices, for instance by exploiting superior parallel operating capabilities, and the like. In this respect the concept of quantum computation has been long proposed in order to exploit quantum effects, such as non-locality, and the like, which may be used to significantly increase overall computational power. For example, the concept of QCA is a widely adapted approach to construct logic gates on the basis of a basic quantum mechanical system. For example, a QCA cell may be implemented on the basis of so-called quantum dots, which may be understood as substantially “zero”-dimensional quantum systems. A quantum dot may be seen as an “artificial atom” of reduced dimensionality, wherein an electrical charge or any other quantum mechanical property may be determined in a highly localized manner, since the quantum dot may represent a potential well for the electrical charge. For example, a quantum dot may be realized by including a small quantity of a material within the substrate, wherein the small quantity of material is appropriate to receive electrical charge, for instance in the form of a single electron or a single hole, thereby resulting in a highly localized electrically distinguishable state for the quantum dot under consideration, while on the other hand, the electrical charge may change its state by transitioning, i.e. tunnelling, from one quantum dot to a neighboring quantum dot.
For example, realization of a quantum dot may be achieved by depositing indium on a GaAs substrate, which results in a concentration of indium material within the substrate, since generally the InAs lattice structure is quite different from a gallium lattice. By using several layers of GaAs pillow-like structures can be obtained, thereby creating an appropriate structure of potentials, which results in a “distribution” of the electrical charge across several dots. Four dots realized in the same layer then constitute a QCA cell, in which two additional electrical charges, for instance in the form of electrons, can populate the quantum dots by tunnelling, thereby imparting a certain electrical charge distribution to the QCA cell. For example, for a square cell configuration the electrostatic force causes the two electrons to occupy antipodal sites within the cell, thereby enabling the distinction between two basically different polarization states.
As shown in FIG. 1A a single cell 101 may be represented by four quantum dots 104A, . . . , 104D, i.e. by four locations, each of which is able to accept an extra electrical charge 102, 103, wherein the charge may change its position on the basis of the potential distribution within a single cell and on the basis of externally acting electrostatic forces. As shown, the two extra electrical charges 102, 103 may result in two different polarization states of the basic cell 101, which may therefore represent two different logic states. For example, the logic state corresponding to the location of the electrical charges as indicated in the left-hand side of the figure may represent the cell 101 being in a logic “0”, while the state represented by cell 101 at the right hand side may be identified as a logic “1”. These states can readily be identified as those states having minimum energy with respect to the resulting electrostatic forces acting between the two additional electrical charges 102, 103.
As is evident, by providing a plurality of basic cells 101, which interact with each other by electrostatic forces, a quantum dot QCA assembly may be obtained. It should be appreciated that the basic cell configuration is selected such that quantum mechanical tunnelling of the electrical charges 102, 103 does not occur between neighboring cells and the interaction between neighboring cells is conveyed by electrostatic forces only. For example, a typical lateral dimension 101D may be in the order of magnitude of 10 nm, while a distance between neighboring basic cells 101 may be in the order of magnitude of several tens of nm.
FIG. 1B schematically illustrates a plurality of basic cells 101A, . . . , 101E, which may be considered as a QCA assembly 100, wherein the logic states of one of the basic cells may be determined by the logic state of the neighboring cells. For convenience, only the quantum dots are illustrated, which actually comprise the localized extra charges 102, 103. As shown, the basic cell 101A is in a polarization state, which corresponds to a logical “0”. On the other hand, the basic cells 101B, . . . , 101E have the localized charges 102, 103 so as to correspond to a logical “1”. As discussed above, the resulting polarization state of any of the basic cells may be considered as being determined by the effect of the electrostatic forces exerted by the surrounding cells. If, for instance, one or more of the basic cells of the assembly 100 may be considered as cells, whose state may be forced into a desired polarization state based on an appropriate mechanism, these cells may be considered as “input” of the assembly 100. It may, for instance, be assumed that the cells 101A, 101D and 101C are forced into the respective polarization states 0, 1, 1 as shown in FIG. 1B. In this case the central cell 101E therefore transitions into the logic state “1” due to the “majority” effect of the resulting combined electrostatic force exerted by the surrounding “input” cells 101A, . . . , 101C on the central cell 101E. Hence, the central cell 101E may be considered as a central “device” representing the result of the logic states input in the assembly 100 by the “input” cells 101A, 101D, 101C. Furthermore, if the cell 101B also represents the basic cell whose polarization state may freely adjust with respect to the surrounding electrostatic forces, its polarization state will be a copy of the state of the central cell 101E, since this cell is the nearest neighbor of the cell 101B. Hence, the cell 101B may represent an “output” of the assembly 100 and may be coupled to another assembly or to any other components so as to provide an appropriate voltage level for about electronic devices.
Based on this “majority” effect appropriate structures for signal processing, i.e. signal propagation and signal manipulation, may be constructed, such as logic gates, thereby realizing computational resources and signal processing capabilities at extremely low power levels.
With reference to FIGS. 1C to 1H some illustrative examples for signal processing on the basis of respective QCA assemblies will now be described, wherein it is assumed that a signal is provided in the form of a bit sequence, i.e., the signal is presented by a sequence of binary logic states.
FIG. 1C schematically illustrates the QCA assembly 100 in the form of a linear configuration including the basic cells 101A, . . . , 101F. As is evident when inducing a logic state “1” at any of the basic cells, this injected logic state will propagate along the linear configuration due to the above described majority effect. For example, when causing the basic cell 101A to take on the logic state “1”, this state will travel through the entire linear configuration at high speed and low power consumption. In this manner linear conductors for conveying a signal in the form of a bit sequence may be established. FIG. 1D schematically illustrates a non-linear configuration, wherein the spatial direction of signal transport may be changed, for instance under a right angle. However, any other spatial configuration may be established. It should be appreciated that, in comparison to a conventional conductive line, problems, such as current crowding, and the like, may be avoided, even if extremely sharp corners have to be implemented, thereby providing for superior design flexibility.
FIG. 1E schematically illustrates the QCA assembly 100 in the form of an inverter, in which the majority effect results in identical polarization states of the basic cells 101A, . . . , 101E, while on the other hand the principle of minimized energy requires the basic cell 101F, and thus any further basic cells immediately adjacent thereto, to take on the complementary polarization stage, thereby achieving a bit inversion.
FIG. 1F schematically illustrates the QCA assembly 100, in which a logic state, for instance input at the basic cell 101A, may be transferred and then output by two different “output” cells 101C and 101D, thereby obtaining a “fan out” function.
FIG. 1G schematically illustrates the QCA assembly 100 in the form of an AND gate, which is accomplished by providing a basic cell 101A having a fixed polarization state or charge distribution, which represents a logic state “0”. On the other hand the basic cells 101B and 101D may represent input cells, in which a desired logic state or bit value is induced. As discussed above, due to the majority effect the central cell 101C and thus the output cell 101E will take on a logic state “1” only when the logic state of both the basic cell 101B and the basic cell 101D is “1”. For any other case the majority effect results in the central cell 101C taking on the logic state “0”.
Similarly FIG. 1H illustrates the QCA assembly 100 in the form of an OR gate, in which the basic cell 101A is in a fixed logic state “1”, while the basic cells 101B and 101D function as input cells, as discussed above. As is evident, due to the majority effect an OR association of the input cells is obtained at the output cell 101E.
The implementation of signal processing capabilities by using QCA assemblies is a very promising approach for overcoming the significant difficulties that are associated with complex signal processing devices based on conventional CMOS technology, in particular, as features, such as parallel processing, and the like, may readily be implemented on the basis of QCA assemblies. One of the most promising technologies for implementing quantum dots and thus QCA assemblies, is the generation of Bose-Einstein condensates, which is frequently applied in order to overcome the significant difficulties in traditional QCA assemblies based on the deposition of indium on a GaAs substrate, as discussed above. However, the generation of a Bose-Einstein condensate requires extremely low temperatures in order to obtain the very unique properties of condensed atoms, each of which has the same quantum states. Therefore, tunnelling and quantum effects may occur at a macroscopic scale, thereby providing advantages with respect to define and detect a corresponding state of the condensate. However, as already mentioned above, the very low operating temperature of approximately 1K makes this approach less than desirable for practical applications.
It is therefore an object of the present disclosure to apply cellular automata assemblies for signal processing while avoiding or at least reducing the effects of one or more of the problems identified above.